{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 9, demo 1\n",
    "\n",
    "Bayesian data analysis\n",
    "\n",
    "Prof Gelman has a jar of coins. He promises that if the students guess how many coins there are, they will get all the coins in the jar. Students discuss and guess different values. Based on these they eventually present their uncertainty about the number of coins as a normal distribution N(160,40). What value they should guess?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import preliz as pz\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# distribution\n",
    "m = 160     # mean\n",
    "s = 40      # std\n",
    "\n",
    "x = np.arange(m-3*s, m+3*s+1)\n",
    "dist = pz.Normal(m, s)\n",
    "px = dist.pdf(x)\n",
    "xpx = x * px"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If students just want to guess right, and they do not care how much money they'll get they should guess the most probable value, i.e. the mode of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = dist.plot_pdf(legend=None)\n",
    "ax.set(xlim=x[[0, -1]], xlabel='number of coins', ylabel='probability')\n",
    "\n",
    "mode = dist.mode()\n",
    "ax.vlines(mode, 0, dist.pdf(mode), colors='C2', ls='--', lw=2, label=f'most probable value = {mode}')\n",
    "plt.legend(bbox_to_anchor=(0.5, 1.02), loc='center');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively students might want to maximize the expected utility of the number coins. Assume that utility of the money is linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the utility\n",
    "plt.plot(x, x)\n",
    "plt.ylabel('utility if guess is correct')\n",
    "plt.xlabel('guess')\n",
    "plt.xlim([x[0], x[-1]])\n",
    "plt.ylim([x[0], x[-1]]);\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If students guess value $a$, given their estimate of the uncertainty, probability that they get $a$ coins is $p(a)$, and expected utility is $a * p(a)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots()\n",
    "\n",
    "ax.plot(x, xpx)\n",
    "ax.set(xlim=x[[0, -1]], ylim=0, xlabel='guess', ylabel='expected utility')\n",
    "\n",
    "mi = np.argmax(xpx)\n",
    "meu = xpx[mi]\n",
    "meux = x[mi]\n",
    "ax.vlines(meux, 0, meu, colors='C2', ls='--', lw=2, label=f'guess which maximises the expected utility = {meux}')\n",
    "\n",
    "plt.legend(bbox_to_anchor=(0.5, 1.02), loc='center');"
   ]
  }
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